Let $p:X\\rightarrow X/A$ be a quotient map, where $A$ is a subspace of $X$. We explore conditions under which $p_*(\\pi_1^{qtop}(X,x_0))$ is dense in $\\pi_1^{qtop}(X/A,*))$, where the fundamental groups enjoy the natural ...

In this talk we are interested to focus on subgroups of topologized fundamental groups and some relationships between generalized covering subgroups and some famous subgroups of the fundamental group equipped with the ...

$ by collapsing each of the sets $A_i$'s to a point, is also locally 1-connected. Moreover, we prove that the induced continuous homomorphism of quasitopological fundamental groups is surjective. Finally, we give some applications to find out some properties...

This paper is devoted to study some topological properties of the SG subgroup, πsg1 (X, x), of the quasitopological fundamental group of a based space (X, x), πqtop1 (X, x), its topological properties as a subgroup of the topological fundamental...

In this paper, by introducing some kind of small loop transfer spaces at a point, we study the behavior of topologized fundamental groups with the compact-open topology and the whisker topology, $\\pi_{1}^{qtop}(X,x_{0})$ ...

Let H be a subgroup of the fundamental group π1(X,x0). In this paper, first, we give a positive answer to a problem presented by Brodskiy et al. in [8, Problem 4.8]. Second, by extending the concept of strong SLT space to ...

For a connected, locally path connected space X , let H be a subgroup of the fundamental group

of X , p1(X ; x ) . We show that there exists an open cover U of X such that H contains the Spanier

group p (U ; ...

In this talk we are interested to focus on open subgroups of topologized fundamental groups

and give some equivalent conditions on a topological space to make sure a subgroup of its

topologized fundamental ...

Let $H$ be a subgroup of $\\pi_{1}(X,x_{0})$. In this paper, we extend the concept of $X$ being SLT space to $H$-SLT space at $x_0$. First, we show that the fibers of the endpoint projection $p_{H}:\\widetilde {X}_{H}\\rightarrow ...